A firm in China produces computer chips at constant marginal cost MC=10 yuan. Ho

Question

A firm in China produces computer chips at constant marginal cost MC=10 yuan. However, with each chip produced, the factory emits pollution that costs society 2 yuan.

a. What is the externality (external cost) of producing computer chips? What kinds of costs might the external costs include (be specific)?

b. What is the private marginal cost of producing chips faced by the firm? What is the social marginal cost ?

c. On the axes below, graph the private and social marginal cost curves. Be sure to label each curve clearly. Also indicate the size of the external cost on the graph.

d. Assume that aggregate demand in the economy is given byP= 20-2Q^d . Graph the demand curve on the graph in part (c) above. Label the demand curve clearly.

e. Calculate the equilibrium price and quantity of chips produced. Label the quantity and the price on the graph in part (c).

f. Calculate the efficient price and quantity of chips. Label the quantity and the price on the graph in part (c). Is higher or lower than ? Why? Is higher or lower than ? Why?

g. Calculate total welfare at equilibrium production, Q^e. You need to calculate an actual number, not just show it on the graph.

h. Calculate total welfare at efficient production, Q*. You need to calculate an actual number, not just show it on the graph.

i. Calculate the size of the deadweight loss incurred for producing at Q^e.

Explanation / Answer

a. When a firm makes computer chips in china. In order to make those chips, it must pay it's workers, invest in new plant equipment and buy your raw materials. Of course each of these costs will be reflected in it's private marginal cost curve. Which, is also firm's supply curve. But further assume, that in producing computer chips, company also generates large amounts of toxic waste. In a free market, an in the absence of any laws to the contrary, company may simply dump these toxic wastes into a nearby river to minimize its costs. Nonetheless, the resulting pollution will not be without cost to the broader society. Children may get leukemia from drinking water from the river. Fisherman may catch less fish because of the toxic waste kill of fish. And homeowners along the river may get sick from the smell. These types of external or spill over effects are called negative externalities.

b. The private marginal cost of producing chips faced by the firm is 10 yuan

and the social marginal cost is 2 yuan

e. Calculate the equilibrium price and quantity of chips produced.

  P= 20-2Q^d

  TR = P*Q = (20-2Q)*Q

MR =dTR/dQ = 20 - 4Q

For equilibrium

MR = MC

20 -4Q = 10

Q = 2.5

P = 20 - 2*2.5 = 15

f. Calculate the efficient price and quantity of chips. Label the quantity and the price on the graph in part (c). Is higher or lower than ? Why? Is higher or lower than ? Why?

For efficient quantity to be produced

MR= MSC

20-4Q= 12

Q = 2

P = P= 20-2*2 = 16

So it is lowr than price in c

g. Calculate total welfare at equilibrium production, Q^e. You need to calculate an actual number, not just show it on the graph.

Total Welfare = producer surplus + consumer surplus

= 1/2(20-15)*2.5 + (16-10)2.5

= 6.25 + 15

= 21.25

For A

h. Calculate total welfare at efficient production, Q*. You need to calculate an actual number, not just show it on the graph.

Total Welfare = producer surplus + consumer surplus

= 1/2(20-16)*2 + (16-12)2

= 4 + 8

= 12

i. Calculate the size of the deadweight loss incurred for producing at Q^e.

Dead weight loss = 1/2(5-2.5)(15-10)

= 6.25

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.