Question

This question introduces a fundamental result of taxation which will revisit in the last chapter. We can already see it at work through the following example: A firm faces the following demand curve: P = 120 – 0.02Q Where Q is weekly production and P is price, measured in cents per unit. The firm’s total cost function is given by TC = 60Q + 25,000. Assume that the firm maximizes profit. a. What is the level of production, price, and total profit per week? (Hint: to answer the question, you need to know MR and MC. In this case, MR = 120 – 0.04Q and MC = 60. [These results can be found by way of calculus, but you are not responsible for knowing this.]) b. If the government decides to levy a tax of 14 cents per unit on this product, what will be the new level of production, price, and profit?

(i) Start by considering that, initially, the consumers must pay the tax to the government.

(Hint: to answer this question, you need to remember that the total price (including the tax) consumers would be willing to pay remains unchanged. Hence the original price is now broken down into two parts: the price received by the suppliers and the tax. The new demand curve is therefore P*+14 = 120 – 0.02Q, where P* is the price received by the suppliers. P* = 106 – 0.02Q. From there, apply the rule that the MR curve has the same intercept but twice the slope of the demand curve: MR = 106 – 0.04Q [a rule that you are not responsible for.]. Then proceed with the standard profit maximization rule.)

Answer 1

P= 120 -0.020 TC = 60Q + 25000 MR = 120 - 0.040 MC = 60 Finding profit maximization price, quantity and profit: MR = MC 120 -0.04Q = 60 Q = 1500 By substituting the value of Q. P = 120 -0.020 P= 120 -0.02*1500 P= $90 Calculation of TR: TR=P*0 TR = 90*1500 TR = 135000

Calculation of TC: TC = 600 + 25000 TC = 60*1500 + 25000 TC = 115000 Calculation of profit: Profit = TR-TC Profit = 135000 - 115000 Profit = 20,000 Thus, the profit maximization price is $90, quantity is 1500 and profit is $20,000. If the government decides to levy a tax of 14 cents per unit on this product, Thus, the new demand curve will be, P*+14 = 120 -0.020 P* = 106 -0.020 TR = 106Q -0.02Q^2 MR = 106 - 0.04Q

Finding profit maximizing price, quantity and profit: MR = MC 106 -0.04Q = 60 Q = 1150 By substituting the value of Q, P= 106 -0.020 P= 106 -0.02*1150 P= 83 Calculation of TR: TR =P*Q TR = 83*1150 TR = 95,450 Calculation of TC: TC = 600 + 25000 TC = 60*1150 + 25000 TC = 94,000

Calculation of profit: Profit = TR - TC Profit = 95,450 - 94,000 Profit = $1450 Thus, the profit maximization price is $83, quantity is 1150 and profit is $1450 after tax is levied.