Consider the purchase contract between the prime contractor and the subcontractor in the monopolistic demand market. The subcontractor's cost function is Ciq, where q is the quantity and C is its marginal cost. i = {H, L} and CH>CL. The marginal cost of the subcontractor is known only to the subcontractor, and the probability that it is CH equals to a. The profit function of the prime contractor is v(q)-t, and the profit function of the subcontractor is t-ciq, where t is the total purchase price paid by the prime contractor to the subcontractor. The subcontractor's retention rate is zero. A. Illustrate the social optimal quantity (q, q) and explain why it is optimal. Under the asymmetric information, illustrate and explain the quantity(q, q) and payment (t), t) that the prime contractor buys from each type of subcontractor to maximize profit. Compare the aprime contractor's profit-maximizing quantity (99) with the socially optimal quantity (q, q) and explain why they differ. B. If the probability that the subcontractor is H-type decreases, how does the profit-maximizing contract offered by the prime firm and the social efficiency change? Explain why. If the marginal cost of the H- type subcontractor increases, how does this change the profit- maximizing contract offered by the prime contractor and the social efficiency, and explain with the help of a diagram why does it so.
Consider the purchase contract between the prime contractor and the subcontractor in the monopolistic demand market. The subcontractor's cost function is Ciq, where q is the quantity and C is its marginal cost. i = {H, L} and CH>CL. The marginal cost of the subcontractor is known only to the subcontractor, and the probability that it is CH equals to a. The profit function of the prime contractor is v(q)-t, and the profit function of the subcontractor is t-ciq, where t is the total purchase price paid by the prime contractor to the subcontractor. The subcontractor's retention rate is zero. A. Illustrate the social optimal quantity (q, q) and explain why it is optimal. Under the asymmetric information, illustrate and explain the quantity(q, q) and payment (t), t) that the prime contractor buys from each type of subcontractor to maximize profit. Compare the aprime contractor's profit-maximizing quantity (99) with the socially optimal quantity (q, q) and explain why they differ. B. If the probability that the subcontractor is H-type decreases, how does the profit-maximizing contract offered by the prime firm and the social efficiency change? Explain why. If the marginal cost of the H- type subcontractor increases, how does this change the profit- maximizing contract offered by the prime contractor and the social efficiency, and explain with the help of a diagram why does it so.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Consider the purchase contract between the prime contractor and the
subcontractor in the monopolistic demand market. The
subcontractor's cost function is Ciq, where q is the quantity and C is
its marginal cost. i = {H, L} and CH>CL. The marginal cost of the
subcontractor is known only to the subcontractor, and the probability
that it is CH equals to a. The profit function of the prime contractor is
v(q)-t, and the profit function of the subcontractor is t-ciq, where t is
the total purchase price paid by the prime contractor to the
subcontractor. The subcontractor's retention rate is zero.
A. Illustrate the social optimal quantity (q, q) and explain why it is
optimal. Under the asymmetric information, illustrate and explain the
quantity(q, q) and payment (t), t) that the prime contractor buys
from each type of subcontractor to maximize profit. Compare the
aprime contractor's profit-maximizing quantity (99) with the
socially optimal quantity (q, q) and explain why they differ.
B. If the probability that the subcontractor is H-type decreases, how
does the profit-maximizing contract offered by the prime firm and the
social efficiency change? Explain why. If the marginal cost of the H-
type subcontractor increases, how does this change the profit-
maximizing contract offered by the prime contractor and the social
efficiency, and explain with the help of a diagram why does it so.
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