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.
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