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Homework answers / question archive / Suppose that Intel has a monopoly in the market for computer chips
Suppose that Intel has a monopoly in the market for computer chips. In order to produce X computer chips, it costs Intel C(x) = 2x?. (a) Find the marginal cost of producing a computer chip for Intel. [2 marks] (b) The demand for computer chips is X=12 – 0.25 P. Find the level of output that maximizes Intel's profits. What price is Intel charging? [6 marks] (c) What level of output would maximize total surplus in the computer chip market?[4 marks] (d) Suppose the government knew the demand and production functions. Find a price regulation the government could impose that would induce Intel to maximize total surplus, i.e., produce the efficient quantity from part (e). [4 marks] (e) If the government subsidized Intel s for every unit of computer chips produced, what quantity would Intel choose as a function of s? Find the choice of subsidy that maximizes total surplus, i.e., induces Intel to produce the efficient quantity from part (e). [6 marks) (f) Both the price regulation policy from part (d) and the subsidy policy from part (e) maximize total surplus. Is there any reason someone might prefer one policy over the other? [3 marks]
a) Marginal cost of producing a chip = 4X
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b) XD = 12 - 0.25P
Thus, P = 48 - 4X (take P on LHS)
Thus, TR = 48X - 4X2
MR = 48 - 8X
Equate, MR = MC (profit maximizing condition)
4X = 48 - 8X
12X = 48
X = 4 units
P = $32 per chip (from the demand function)
At the profit maximizing output of 4 units, Intel charges $32 per chip.
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c) Maximum Surplus is where P = MC
Thus, 48 - 4X = 4X
48 = 8X
X = 6 units
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d) At X = 6 units, P = $24 per chip (from the demand function)
Hence, government should impose a maximum price of $24 per chip.
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e) If a subsidy is provided, Intel will produce 6 units of chips.
A subsidy of $8 per chip should be given.
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f) A subsidy is considered to be a more efficient way than a price ceiling. A subsidy is a market based mechanism, while a price ceiling is a control on prices. A subsidy will lead to higher consumer and producer surplus both. A price ceiling will lead to higher consumer surplus, but lower producer surplus - and also create a shortage in the market.
Thus, the subsidy is more preferred.
