. Gemini Robotics, Inc. is a monopoly firm in the market for home robots. The ow
ID: 1115054 • Letter: #
Question
. Gemini Robotics, Inc. is a monopoly firm in the market for home robots. The owner-manager of Gemini founded the home robot industry in 2015 on the basis of the following forecasted demand function for home robots in 2015: Q=9,000-0.2P + 0.2 M + 56/, where O is the number of robots sold, M is the average annual income of potential buyers, and Ps is the price of butlers (in dollars per day). In 2015, the owner-manager of Gemini expects M = $50,000/year and P,-$125/day. a. The forecasted demand function in 2015 is Q= b. The inverse demand function is P= c. The marginal revenue function is MR= Suppose Gemini Robotics faces the following estimated average variable cost function: AVC-40,000-2000+g d. The estimated marginal cost function is SMC = c. The optimal level of output for 2015 is f. The price of a home robot in 2015 will be S g. If Gemini Robotics expects fixed costs in 2015 to be S15 million, then it can expect to ts. carn a profit (loss) of SExplanation / Answer
Q3
Answer
a)
The demand function is
Q=9000-0.2P+0.2*50000+56*125
Q=26000-0.2P
b)
inverse demand function is nothing but in term of Q
P=130000-5Q
c)
TR=P*Q=130000Q-5Q^2
MR=dTR/dQ=130000-10Q
d)
VC=AVC*Q=40000Q-200Q^2+Q^3
SMC=dVC/dQ=40000-400Q+3Q^2
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