question

3.2 Why, under conditions of perfect competition, does the marginal revenue of the firm equal its output price?

answer

Because firms are price takers in the perfectly competitive market they must accept the price determined by the intersection of supply and demand. That price is fixed (all else equal) thus marginal revenue = price.

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3.3 List ALL of the assumptions made to construct our model of the perfectly competitive firm. Do not include the assumptions that define the perfectly competitive market

answer

1. The firm has a long-run production function x = f (ℓ,k) based on a given technology.* 2. The long-run production function has the following properties:

2a. Zero input produces zero output [f (0,0) = 0], and nonnegative input produces nonnegative output [f (ℓ,k) ≥ 0 for all (ℓ,k) ≥ 0].

2b. It is continuous and all marginal products can be calculated.

2c. If ridge lines exist, all marginal products are positive and all isoquants are strictly convex between the ridge lines up to an intersection point if there is one.

2d. If ridge lines do not exist, all marginal products are positive and all isoquants are strictly convex everywhere, and no isoquant touches the co-ordinate axes.

3. Long-run and short-run total cost curves appear as drawn in class so that average and marginal cost curves can be determined and have the shapes attributed to them.

4. The firm hires inputs and produces output so as to maximize profit.

*The short-run production function is obtained from the long-run production function by fixing k at some value k 0 , that is, x = f (ℓ,k 0 ).

2a. Zero input produces zero output [f (0,0) = 0], and nonnegative input produces nonnegative output [f (ℓ,k) ≥ 0 for all (ℓ,k) ≥ 0].

2b. It is continuous and all marginal products can be calculated.

2c. If ridge lines exist, all marginal products are positive and all isoquants are strictly convex between the ridge lines up to an intersection point if there is one.

2d. If ridge lines do not exist, all marginal products are positive and all isoquants are strictly convex everywhere, and no isoquant touches the co-ordinate axes.

3. Long-run and short-run total cost curves appear as drawn in class so that average and marginal cost curves can be determined and have the shapes attributed to them.

4. The firm hires inputs and produces output so as to maximize profit.

*The short-run production function is obtained from the long-run production function by fixing k at some value k 0 , that is, x = f (ℓ,k 0 ).

question

3.5 Think of a firm in a perfectly competitive market without free entry or exit:

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1. Does profit maximization in the long- or short-run guarantee by itself that the firm produces an output at the minimum point of its long- or short-run average cost curves? Why or why not?

No, bc producing there doesn't guarantee that were gonna be at the profit maximizing point, wont guarantee that marg cost = marg revenue.

2. Does profit maximization in the long- or short-run imply that the firm produces an output for which revenue is maximized? Why or why not?

We could infinitely increase our revenue, but avg cost would eventually be greater than rev, profits shrink faster and faster. Since we're just concerned with most revenue, we will incur very large costs, ruining profits.

3. If the firm hires inputs so as to minimize the cost of producing each output, it is necessarily producing the profit-maximizing output? Why or why not?

No, we need information about our revenue, because we need enough revenue to make profits when we minimize costs.

No, bc producing there doesn't guarantee that were gonna be at the profit maximizing point, wont guarantee that marg cost = marg revenue.

2. Does profit maximization in the long- or short-run imply that the firm produces an output for which revenue is maximized? Why or why not?

We could infinitely increase our revenue, but avg cost would eventually be greater than rev, profits shrink faster and faster. Since we're just concerned with most revenue, we will incur very large costs, ruining profits.

3. If the firm hires inputs so as to minimize the cost of producing each output, it is necessarily producing the profit-maximizing output? Why or why not?

No, we need information about our revenue, because we need enough revenue to make profits when we minimize costs.

question

3.7 Give a step-by-step argument to show how the perfectly competitive firm's input demand and output supply functions are derived from the assumptions of our longrun model of that firm. (In your answer, start with the production function and include ridge lines, cost minimization, the expansion path, and cost and revenue functions.)

answer

1. If ridge lines exist, eliminate the regions outside of the area between them and beyond The intersection point if there is one.

2. Using input price information (long run) or fixed capital information 𝑘𝑘� (short-run), calculate the expansion path and confine attention to it.

3. Using the production function and expansion path information, calculate all cost functions and curves expressing cost as a function of output.

4. Using output price information, calculate all revenue functions and curves.

5. Using cost and revenue information, calculate the profit-maximizing output 𝑥𝑥0.

6. From the intersection of the isoquant relating to the profit-maximizing output and the expansion path, calculate the profit-maximizing input quantities - (𝑙𝑙 0, 𝑘𝑘0) in the long run and 𝑙𝑙 0 in the short run - as shown in the diagrams below

2. Using input price information (long run) or fixed capital information 𝑘𝑘� (short-run), calculate the expansion path and confine attention to it.

3. Using the production function and expansion path information, calculate all cost functions and curves expressing cost as a function of output.

4. Using output price information, calculate all revenue functions and curves.

5. Using cost and revenue information, calculate the profit-maximizing output 𝑥𝑥0.

6. From the intersection of the isoquant relating to the profit-maximizing output and the expansion path, calculate the profit-maximizing input quantities - (𝑙𝑙 0, 𝑘𝑘0) in the long run and 𝑙𝑙 0 in the short run - as shown in the diagrams below

question

3.8 Explain how a change in

the price of labor alone,

the price of labor alone,

answer

1. Change in the input price ratio, and hence in the slope of the iso-cost lines.

2. Changes in the locations of the tangencies between iso-cost lines and isoquants

3. Change in the long-run expansion path

4. Changes in the long-run cost curves - in particular, in the long-run marginal cost curve.

5. Change in the intersection of the long-run marginal cost curve and the marginal revenue line, and hence in the profit-maximizing output

6. Change in the isoquant relating to the profit-maximizing output

7. Since there is a new long-run expansion path (step 3) and a new isoquant relating to the profit-maximizing output (step 6), there is a new intersection of them, and hence a change in the profit-maximizing quantities of labor and capital inputs

2. Changes in the locations of the tangencies between iso-cost lines and isoquants

3. Change in the long-run expansion path

4. Changes in the long-run cost curves - in particular, in the long-run marginal cost curve.

5. Change in the intersection of the long-run marginal cost curve and the marginal revenue line, and hence in the profit-maximizing output

6. Change in the isoquant relating to the profit-maximizing output

7. Since there is a new long-run expansion path (step 3) and a new isoquant relating to the profit-maximizing output (step 6), there is a new intersection of them, and hence a change in the profit-maximizing quantities of labor and capital inputs

question

3.8 the price of output alone

answer

1. No change in isoquant-isocost tangencies, the long-run expansion path, or long-run cost curves

2. Changes in the revenue curves - in particular, in the marginal revenue curve

3. Change in the intersection of the long-run marginal cost curve and the marginal revenue line, and hence in the profit-maximizing output

4. Change in the isoquant relating to the profit-maximizing output

5. Change in the intersection of the long-run expansion path and the isoquant relating to the profit - maximizing output, and hence a change in the profit-maximizing quantities of labor and capital inputs

2. Changes in the revenue curves - in particular, in the marginal revenue curve

3. Change in the intersection of the long-run marginal cost curve and the marginal revenue line, and hence in the profit-maximizing output

4. Change in the isoquant relating to the profit-maximizing output

5. Change in the intersection of the long-run expansion path and the isoquant relating to the profit - maximizing output, and hence a change in the profit-maximizing quantities of labor and capital inputs

question

3.10 In the short run, under what conditions relating to its output price and average variable cost should a perfectly competitive, profit-maximizing firm continue to produce and sell output when it is losing money (i.e., has negative profit)? Why?

answer

Need to cover fixed costs. If AVC=MC=MR, then we shut down. But if we stop producing at that point, we will not be covering fixed costs.

Graph in notebook.

Graph in notebook.

question

3.10 Why in the short run, can it not go out of business?

answer

A business can only go out of business in the long run because it can only sell its capital stock in the long run. Can't go out of business in the short run because it can't sell its capital stock in the short run.

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3.11 Explain why the short-run output supply curve of the perfectly competitive, profit-maximizing firm is the firm's short-run marginal cost curve above minimum average variable cost.

answer

MC = MR determines our output level

Wherever price falls along mc curve, sets our level of output

That intersection is potential site of profit maximizing point.

Anywhere below MR = AVC : doesn't happen because we shut down.

Anywhere above MR = AVC could be site that determines our level of output

Wherever price falls along mc curve, sets our level of output

That intersection is potential site of profit maximizing point.

Anywhere below MR = AVC : doesn't happen because we shut down.

Anywhere above MR = AVC could be site that determines our level of output

question

3.12 Explain why abnormal profits earned and losses incurred by perfectly competitive, profit-maximizing firms cannot be present at long-run equilibrium.

answer

Can't be present because firms, in the long run, will enter the market increasing the total market wide output which means that supply increases and market price decreases, until we return to normal profits.

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3.13 Explain why the perfectly competitive firm at long-run equilibrium produces an output for which long-run average cost is minimized. Is this output profit maximizing? Why or why not?

answer

Firms will enter in until MR is low enough that they are at a loss. Equilibrium will be at cost minimizing point. The output will be profit maximizing until something changes in the cost structure.

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3.14 In a perfectly competitive market, what is the difference between the way market price is determined in the short run and the long run?

answer

In the short run, market price is determined by the interaction of the forces of supply and demand as described in lecture notes #3.

In the long run, market price is determined by the costs of production, that is, by input prices and how, through technology or the production function, lead to production costs.

In the long run, market price is determined by the costs of production, that is, by input prices and how, through technology or the production function, lead to production costs.

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3.15 Think of a decreasing cost, perfectly competitive industry and a representative firm in that industry at long-run equilibrium. Suppose the demand for that industry's output increases. Describe the steps by which the industry and representative firm adjust to a new long-run equilibrium. How does the new equilibrium compare with the old? Please include diagrams of the industry and representative firm in your answer.

answer

When firms enter the market they demand more inputs and so costs go up. This squeezes abnormal profits. Additional demand for inputs, the price of the inputs increases. As a result the output price ends up higher than it would have been previously. In a decreasing cost industry, costs would go down like with a new technology.

Graphs in notebook

Graphs in notebook

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3.16 Explain why, in the short run, the perfectly competitive, profit-maximizing firm should hire labor up to the point at which its marginal revenue product (or value of marginal product) equals the price of labor (wage).

answer

They should hire up until the point where they are not getting more revenue per unit hired. Don't go past bc the additional cost is then greater than the additional value we get from the worker. Price vs marginal product

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3.17 Explain why the short-run labor demand curve of the perfectly competitive, profit-maximizing firm is that firm's marginal revenue product (or value of marginal product) curve.

answer

Since val of marginal product relates price of labor to labor hired we can consider it a demand curve for labor by the firm

question

3.18 Draw a diagram showing the perfectly competitive, profit-maximizing firm's long-run demand curve for labor in relation to its marginal revenue product (or value of marginal product) curves. Make your diagram large and label all curves, axes, and points. Explain why the long-run demand curve for labor is related to more than one marginal revenue product curve.

answer

You get multiple demand curves based on the capital stock selected. Find profit maximizing points along them. All the individual short run labor demand curves, one point per curve that is the profit maximizing point. Select the points out of all the individual demand curves.

Graph in notebook

Graph in notebook