Question

Giant Screen TV, Inc., is a Miami-based importer and distributor of 60-inch screen HDTVs for residential and commercial customers. Revenue and cost relations are as follows:

TR = $4,500Q - $0.1Q²

TC = $2,000,000 + $1500Q + $0.5Q²

1. Calculate output, price and profit at the average cost-minimizing activity level.
2. Calculate output, price and profit at the profit-maximizing activity level.
3. Calculate the level of output and price that will maximize sales revenue. What is the profit associated with this activity level?
4. Plot Giant Screen’s demand curve, marginal revenue curve, marginal cost curve, and average cost curve on the same graph (quantity on the horizontal axis). Show your graphical solutions to part A, B, and C on this graph.

Answer 1

a) average cost minimizes at MC=AC

average cost= total cost/ quantity

=2000000/q + 1500 + 0.5q

marginal cost = 1500 + q (differentiation of total cost equation)

so equating both equations we get

2000000/q + 1500 +0.5q = 1500 + q

q= 2000

At q = 2000

TC= 2000000+ 1500*2000 + 0.5*2000²

=7000000

TR= 4500*2000 - 0.1*2000²

= 8600000

profit = TR-TC

= 8600000-7000000

= 1600000

TR= price*quantity

8600000= P*2000

P= 4300

b) profit maximize at MR=MC

MR= 4500-0.2*Q (by differentiating TR equation)

MC= 1500+Q ( by differentiating TC equation)

MR=MC

4500-0.2*q= 1500+q

Q= 2500

AT Q= 2500

TR= 4500*2500-0.1*2500²

=10625000

TC= 2000000+ 1500*2500 + 0.5*2500²

= 8875000

profit= TR-TC

= 10625000-8875000

= 1750000

TR= price *quantity

10625000= p*2500

P= 4250

c) sales revenue maximize where MR= 0

MR= 4500-0.2q= 0

q= 22500

TC= 2000000 + 1500*22500+ 0.5* 22500²

= 288875000

TR= 4500*22500-0.1*22500²

= 50625000

TR= price*quantity

50625000=p*22500

P= 2250

profit = TR-TC

= 50625000-288875000

= -238250000 ( losses where sales revenue is maximize)

d)

NOTE demand curve is relation between price and quantity

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