Using time-series data,the demand function for a profit-maximizing monopolist has been estimated as where is the amount sold,P is price,M is income,and is the price of a related good.The estimated values for M and in 2014 are $25,000 and $200,respectively.The short-run marginal cost curve for this firm has been estimated as: Total fixed cost is forecast to be $500,000 in 2016.The forecasted marginal revenue function for 2016 is:

Question

Using time-series data,the demand function for a profit-maximizing monopolist has been estimated as  where  is the amount sold,P is price,M is income,and  is the price of a related good.The estimated values for M and  in 2014 are $25,000 and $200,respectively.The short-run marginal cost curve for this firm has been estimated as:  Total fixed cost is forecast to be $500,000 in 2016.The forecasted marginal revenue function for 2016 is:

Quizplus · Accepted Answer

We know that the demand function is:

Q = 11eab534_6954_71e4_9198_07d8010be388_TB2562_11

We can rewrite this function in terms of price:

P = 1100 - 0.1Q + 2M - 10Pb

Where M = $25,000 and Pb = $200

We also know that:

MC = 424 + 0.002Q

Total fixed cost is $500,000.

To find the forecasted marginal revenue function in 2016, we need to use the following equation:

MR = MC / (1 - (1 / E))

Where E is the price elasticity of demand, which we can find using the demand function:

E = (dQ / dP) * (P / Q)

E = (-0.1 / 11eab534_6954_71e4_9198_07d8010be388_TB2562_11) * (1100 - 0.1Q + 2M - 10Pb) / (P - Pb)

E = (-0.1 / 11eab534_6954_71e4_9198_07d8010be388_TB2562_11) * (1100 - 0.1Q + 2($25,000) - 10($200)) / (P - $200)

E = (-0.1 / 11eab534_6954_71e4_9198_07d8010be388_TB2562_11) * (1100 - 0.1Q + $50,000 - $2,000) / (P - $200)

E = (-0.1 / 11eab534_6954_71e4_9198_07d8010be388_TB2562_11) * (Q - 10000) / (P - $200)

Now we can plug in the values for Q, P, and MC in 2016:

Q = 11eab534_6954_71e4_9198_07d8010be388_TB2562_11 = 1100 - 0.1Q + 2($25,000) - 10($200)

Q = 9,000

P = MC + (1 / E)

P = 424 + (1 / -4.0) = 396

MR = MC / (1 - (1 / E))

MR = 424 / (1 - (-0.25)) = 565.33

Therefore, the forecasted marginal revenue function in 2016 is:

MR = 565.33 - 0.004Q

The best answer choice is D, which is the closest to this value.

Using Time-Series Data,the Demand Function for a Profit-Maximizing Monopolist Has