High School

**Problem 1:**

A profit-maximizing monopolist has the cost schedule \(c(y) = 40y\). The demand for her product is given by \(y = \frac{600}{p^4}\), where \(p\) is her price. Suppose the government tries to get her to increase her output by giving her a subsidy of $21 for every unit that she sells. What effect would the subsidy have on her price?

Select one:
a. Decrease her price by $28.
b. Decrease her price by $21.
c. Leave her price unchanged.
d. Decrease her price by $49.
e. Decrease her price by $10.50.

**Problem 2:**

A profit-maximizing monopolist faces a downward-sloping demand curve that has a constant elasticity of -4. The firm finds it optimal to charge a price of $24 for its output. What is its marginal cost at this level of output?

Select one:
a. $24
b. $48
c. $18
d. $10
e. $55

**Problem 3:**

The 130 campers at Bear Creek Campground love their own campfires but hate the smoke from their neighbors' campfires. Each camper's utility function is \(U = 17f - f^2 - s\), where \(f\) is the number of hours her own campfire burns per day and \(s\) is the amount of smoke in the air. It happens that \(s\) is 7 times the average amount of hours that campers use their fires. How many hours of campfire per day should the authority allow each camper in order to make the typical camper as well off as possible?

Select one:
a. 3
b. 5
c. Campers will be best off if they are free to choose their own amounts of campfire.
d. 8.50
e. 6

Answer :

Final answer:

The profit-maximizing monopolist will decrease her price by an amount less than $21 if she receives the subsidy.

Explanation:

To determine the effect of the subsidy on the monopolist's price, we need to analyze how the subsidy affects the monopolist's profit-maximizing decision.

First, let's understand the monopolist's profit-maximizing decision without the subsidy. The monopolist maximizes profit by setting marginal cost equal to marginal revenue. In this case, the cost schedule is c(y) = 40y, which means the marginal cost is constant at $40 per unit.

The demand function is y = 600/p^4, which means the monopolist's marginal revenue is the derivative of the demand function with respect to quantity, multiplied by the price. Taking the derivative of the demand function, we get dy/dp = -2400/p^5.

Setting marginal cost equal to marginal revenue, we have 40 = -2400/p^5 * p. Simplifying the equation, we get p^6 = -60.

Since price cannot be negative, we can ignore the negative solution. Taking the sixth root of both sides, we get p = (-60)^(1/6) ≈ 2.63.

So, without the subsidy, the monopolist would set the price at approximately $2.63.

Now, let's consider the effect of the subsidy. The subsidy of $21 for each unit sold means the monopolist will receive an additional $21 for each unit sold. This effectively reduces the monopolist's cost by $21 per unit.

With the reduced cost, the monopolist can lower the price and still maintain the same level of profit. The exact amount by which the price will decrease depends on the elasticity of demand.

Since the question does not provide information about the elasticity of demand, we cannot determine the exact decrease in price. However, we can conclude that the monopolist will decrease her price by an amount less than $21, as the subsidy reduces her cost and allows her to lower the price while maintaining profit.

Learn more about effect of subsidy on monopolist's price here:

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