Question

3) Kites are manufactured by identical firms. Each firm's total and marginal cost functions for weekly production are given by TC=0.01q2+100MC=0.02q​ In the long-run equilibrium, how many kites will each firm produce? Describe the long-run supply curve for kites. a. Suppose the weekly demand for kites is given by QD​=4000−1000P. How many kites will be sold? How many firms will there be in the kite industry? b. Suppose that the weekly demand for kites suddenly goes up to QD​=5000−500P. In the very short run, when it is impossible to manufacture any more kites than those produced for that weck, what will the price of kiter be? How much profit will cach kite maker cam? In the market short run, what will the price of kites be? How much profit will cach kite maker carn'? d. In the market long run, what will the price of kites be? How many new firms will enter the kite-making industry? How much profit will they carr? Be sure to show your work.

Answer 1

To determine the long-run equilibrium for each firm's production of kites, we need to find the level of output where marginal cost (MC) equals marginal revenue (MR). In perfect competition, firms maximize their profit by producing at the level where MC = MR.

Given the marginal cost function MC = 0.02q, we equate it to the marginal revenue, which is equal to the market price (P) in perfect competition. So, we have:

0.02q = P

Now, we need to find the price at which the quantity demanded (QD) equals the quantity supplied (QS) in the market. To do this, we set QD equal to QS:

QD = QS

Substituting the demand function QD = 4000 - 1000P into the equation, we get:

4000 - 1000P = QS

Now, we can solve for the price (P):

4000 - 1000P = 0.02q

Simplifying further:

1000P = 4000 - 0.02q

P = (4000 - 0.02q) / 1000

Now, we can substitute the value of P into the equation for MC to find the level of output (q):

0.02q = P

0.02q = (4000 - 0.02q) / 1000

Solving for q:

0.02q = 4 - 0.00002q

1.00002q = 4

q = 4 / 1.00002

q ≈ 3999.8

In the long-run equilibrium, each firm will produce approximately 3999.8 kites.

The long-run supply curve for kites in perfect competition is horizontal at the minimum average total cost (ATC) of the firms. This is because in the long run, firms have enough time to adjust their inputs and optimize their production processes, leading to production at the lowest possible cost.

a. To find the number of kites sold and the number of firms in the kite industry, we substitute the price (P) into the demand function QD = 4000 - 1000P:

QD = 4000 - 1000P

QD = 4000 - 1000(4000 - 0.02q) / 1000

Simplifying:

QD = 4000 - 4000 + 0.02q

QD = 0.02q

Since q represents the output per firm and we know that each firm produces around 3999.8 kites, we can substitute this value:

QD = 0.02 * 3999.8

QD ≈ 79.996

Approximately 80 kites will be sold. To find the number of firms in the kite industry, we divide the total quantity supplied by the output per firm:

QS = 3999.8

Number of firms = QS / q

Number of firms = 3999.8 / 3999.8

Number of firms = 1

b. In the very short run, when it is impossible to manufacture any more kites than those produced for that week, the price of kites will be determined by the demand and supply conditions. With the demand function QD = 5000 - 500P, we can find the equilibrium price:

QD = QS

5000 - 500P = QS

Substituting the supply quantity from above:

5000 - 500P = 3999.8

Solving for P:

500P = 5000 - 3999.8