A firm faces the following average revenue (demand)
curve: P = 120- 0.02Q
where Q is weekly production and P is price, measured in cents per unit. The firm”s cost function is given by C = 60Q + 25,000.Assume that the firm maximizes profits.
a. What is the level of production, price, and total profit per week?
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?
a. Profit maximisation is where , Marginal
cost = Marginal Revenue Marginal revenue is twice the slope of demand curve so, Original demand curve is = 120-0.02Q, so MR will be= 120-
0.04Q and MC is slope of total cost curve so total cost =
60Q 25000 So MC will be 60 Profit is when MR=MC So, 120-0.04Q=60 Therefore Q= 1500 , i.e Level of production = 1500 units Price = P = 120-0.02×1500 Price= 90 cents Profit= Total Revenue- Total Cost Total revenue= Price x Quantity ,= 90 x 1500= 135000 Total cost= 60Q 25000, = 60 x 1500 25000, =…
5000 Total profit= 135000-115000 Total Profit=
20000 b. With the
increase in the tax of 14 cents the MR will change ,i.e., New MR= 120-0.04Q-Tax(14) MR= 120-0.04Q-14 MC will remain same 60 Profit maximisation output= 120- 0.04Q-14= 60 Output will be Q= 1,150
units New price =
120-0.02×1150-14, = 83 cents Total Revenue= (83
x 1150)- ( 60 x 1150 25000)= 1450