DQ
From the scenario, assume Katrina's Candies operates in an imperfectly competitive market structure and faces the following weekly demand and short-run cost functions: (VC is variable cost, MC is marginal cost, and FC is fixed cost)
P = 50-0.01Q and MR = 50-0.02Q (Note that the P equation is the demand curve equation)
VC = 20Q+0.006665 Q2, MC=20 + 0.01333Q, and FC = $5,000 (Note that TC (total cost) = FC + VC)
Where price is in $ and Q is in kilograms. All answers should be rounded to the nearest whole number.
Algebraically, determine what price Katrina's Candies should charge in order for the company to maximize profit in the short run.
Determine the quantity that would be produced at this price and the maximum profit possible.
Suppose Katrina's Candies is a monopolist. Instead of maximizing profit in the short run, the firm prefers to use "limit pricing" to keep potential competitors out of the market. What should Katrina's limit price be? Under what conditions would it be an effective deterrent? (Hint: To find the limit price, PL, set ATC = MC and solve for Q. Next, substitute this value of Q into the P equation to solve for PL.
The limit price strategy will be an effective barrier to entry as long as PL is below the potential competitor's price. )
Option 1:
Consider the cost data below:
|
TC
|
Output (Q)
|
|
560
|
50
|
|
790
|
100
|
|
1200
|
150
|
|
1810
|
200
|
|
2550
|
250
|
|
3620
|
300
|
|
4650
|
350
|
|
6210
|
400
|
Using regression analysis, estimate the total cost function assuming a quadratic function is the best fit for the data: (Hint: You must create the variable Q2 and add it to your data set. ) TC = a + b1Q + b2Q2
What is the average cost (AC) function: (Hint AC = TC/Q)?
Assuming the marginal cost (MC) function is MC = -1.84 +0.08Q, what output level minimizes average costs (AC)? (Rounding to 2 decimal places)
What is the minimum average cost at this output level?
If the market price is $5 and is expected to be this price for the unforeseeable future, should this product continue to be produced?
* Hint for option 1: You should generate the following regression equation: TC = 571.96 - 1.84Q + 0.04Q2
The key to finding this equation is to create a third data column where all the values of Q are squared (Q2) and then regress TC (the Y variable) against Q and Q2 (the X variables).
Option 2:
Identify the criteria for a "shut down" and apply it to the following scenario: Suppose a firm sells 500 units per month at $50 per unit. Its fixed costs per month are $30,000 and its variable costs per month are $15,000. Would you advise this firm to continue operating in the short run? Why or why not?