Consolidated Sugar Company sells granulated sugar to both retail grocery chains
ID: 1123110 • Letter: C
Question
Consolidated Sugar Company sells granulated sugar to both retail grocery chains and commercial users (e.g., bakeries, candy makers, etc.). The demand function for each of these markets is:
Retail grocery chains: P1 = 90 - 4q1
Commercial users: P2 = 50 - 2q2
where P1 and P2 are the prices charged and q1 and q2 are the quantities sold in the respective markets. Consolidated's total cost function (which includes a "normal" return to the owners) for granulated sugar is
TC = 25 + 10(q1 + q2 )
(c) Assuming that Consolidated is required to charge the same price in each market, what are the profit-maximizing price and output levels? What is Consolidated's total profit under this condition?
Answer =(c) q1* = 13.33, q2* = 6.67; p = $36.38; p = $508.
please show all steps
Explanation / Answer
q1 = (90 - p1)/4
q2 = (50 - p2)/2
Q = q1 + q2
p1 = p2 = p
Q = (190 - 3p)/4
p = (190 - 4Q)/3
Total revenue = pQ = (190Q - 4Q2)/3
MR = d(pQ)/dQ = 190/3 - 8Q/3
MC = d(TC)/dQ = 10
Profit is maximized where MR = MC :
160/3 = 8Q/3
Q = 20 and p = $36.67
Using p = 36.67 in equations of q1 and q2:
q1 = 13.33 and q2 = 6.67
Profit = TR - TC
Profit = 36.67 x 20 - 25 - 10 x 20 = $508.33