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Chapter 25: Problem 8

The demand for gummy bears is given by \\[ g=200-100 P \\] and these confections can be produced at a constant marginal cost of \(\$ .50\) a. How much will Sweettooth, Inc., be willing to pay in bribes to obtain a monopoly con cession from the government for gummy bear production? b. Do the bribes represent a welfare cost from rent seeking? c. What is the welfare cost of this rent-seeking activity?

Short Answer

Expert verified
b. Do the bribes represent a welfare cost from rent-seeking? c. Calculate the welfare cost of this rent-seeking activity.

Step by step solution

01

Find the total revenue function

Revenue is the price times the quantity sold. Using the given demand function, \(g=200-100P\), we can express revenue as \(R = Pg = P(200-100P)\).
02

Find the total cost function

The marginal cost is a constant \(0.50\) per gummy bear. To find total cost, multiply the constant marginal cost by the number of gummy bears produced, \(g\). Thus, the total cost function is \(C = 0.50g\).
03

Find the profit function

Profit is defined as total revenue minus total cost. Using the revenue and cost functions from Steps 1 and 2, we can write the profit function as \(\pi = R - C = P(200-100P) - 0.50g = P(200 - 100P) - 0.50(200 - 100P)\).
04

Maximize profit

To maximize profit, we will find the first derivative of the profit function with respect to price and set it equal to zero: \(\frac{d\pi}{dP} = \frac{d}{dP}[P(200 - 100P) - 0.50(200 - 100P)] = 0\). Solve for the optimal price \(P\) and then find the corresponding quantity \(g\).
05

Calculate monopoly profit

Substitute the optimal values of \(P\) and \(g\) back into the profit function to find the monopoly profit.
06

Answer part (a)

The monopoly profit found in Step 5 is the maximum amount Sweettooth, Inc. would be willing to pay in bribes to obtain a monopoly concession. This is because if they pay more than this amount, they would make a loss.
07

Answer part (b)

Bribes represent a welfare cost from rent-seeking if the resources spent on bribes could have been put to more productive use. In this case, it could be argued that the bribes are indeed a welfare cost, as the resources used for bribing could potentially have been used for investing in research and development or other ways to improve the company and the product.
08

Answer part (c)

The welfare cost of rent-seeking is equal to the deadweight loss created by the monopoly. To calculate the deadweight loss, find the consumer surplus under monopoly pricing and subtract it from the consumer surplus under competitive pricing (when price is equal to marginal cost). Then, subtract the additional profit made by the monopolist as a result of the rent-seeking from the deadweight loss.

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Most popular questions from this chapter

Suppose seven individuals constitute a society in which individuals cast votes for their most preferred social arrangement and that the arrangement with the greatest number of votes is always chosen. Devise an example of individual rankings of the three states \(A, B,\) and Csuch that state \(A\) is chosen when all three states are available but that state \(B\) is chosen if the "irrelevant" alternative Cis not available. (This amounts to showing that the constitution of this society does not obey Axiom 4 in Arrow's list.) How reasonable is your example? What does it indicate about the nature of Arrow's axiom?

Suppose there are three individuals in society trying to rank three social states \((A, B,\) and C). For each of the methods of social choice indicated, develop an example to show how (at least) one of the Arrow axioms will be violated. a. Majority rule without vote trading. b. Majority rule with vote trading. c. Point voting where each voter can give \(1,2,\) or 3 points to each alternative and the al ternative with the highest point total is selected.

In the 1930 s several authors suggested a "bribe criterion" for judging the desirability of social situations. This welfare criterion states that a movement from social state \(A\) to state \(B\) is an improvement in social welfare if those who gain by this move are able to compensate those who lose sufficiently so that they will accept the change. Compensation does not actually have to be made; it is only necessary that it could be paid. If the compensation is actually made, this criterion reduces to the Pareto definition (some individuals are made better off without making anyone worse off). Hence, the criterion is novel only in that compensation is not paid by the gainers to the losers. In such a situation, does the bribe criterion seem to be "value- free," or does the criterion seem somehow to favor those who are initially rich? Can you give some simple examples?

Suppose voters based their decisions on the ratio of utilities received from two candidates that is, Equation 25.6 would be Show that the results from a game involving net value platforms would in this case maximize the Nash Social Welfare function \\[ s w=Y l u_{l} \\]
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