3. Imagine there is a monopolist with a cost function of C = 500 + 5Q+ Q, and a demand function of P = 50 - 1/20 a. State the firm's fixed costs. b. Differentiate the cost function to find the marginal cost function. c. Multiply both sides of the demand function by Q. This is the revenue function. d. Differentiate the revenue function to find the marginal revenue function. e. Use the rule that maximum profit is when MC = MR to find the profit-maximising Q. f. Now use the demand function to find the market price at this Q. g. Use your results to find the firm's total revenue at this Q. h. Use the cost function to find the firm's total cost at this Q. Hence find the firm's profit. i. 4. Taking the same firm: a. Find the firm's average cost function, by dividing both sides of the cost function by Q. b. Differentiate the average cost function you have found, and set the result equal to zero. c. Then solve for Q to find the level of Q at which average cost is minimised. d. Use the value for Q that you have just found in the average cost function, to compute the minimum average cost. e. Now use the demand function to find the quantity demanded if the good were sold at that minimum average cost. f. Compare the results you found in parts (c) and (e). Comment on what you have found, thinking about market structure and minimum efficient scale. 5. Again taking the same firm: a. Use graph paper to carefully hand-draw the firm's demand curve, MC curve, and MR curve. Your x-axis should show Q and go from 0 to 50. Your y-axis should show P (and C) and also go from 0 to 50. You will get credit for a neat diagram. b. Use dotted lines and shading to show the areas of consumer surplus, producer surplus, and deadweight loss. c. Using the geometric rule that the area of a triangle is equal to height x width x , find the area of deadweight loss. You will get extra marks for using demand, MC and MR to be precise about the height and width of the triangle. For example, MR = MC will give you the bottom point of the triangle (as this is where the two lines cross).