Question

Below find the demand for meals at a resturant:

daytime demand : Pn=20 -.0125 Qd

night demand Pn=40- .025Qn

ATC=MC=3.00

Claculate the daytime price and quantity of meal sold:

Pd=____________

Qd=___________

Calculate the nighttime price and quantity of meal sold

Pn=_______

Qn=______

what is the profit earned by charging these prices?

Answer 1

Daytime

Demand function

P = 20 - 0.0125Q

Profit is maximized where marginal revenue is equal to marginal cost, we have the marginal cost so we have to find out marginal revenue

To find marginal revenue we will use demand function by doubling the coefficient of Q

MR = 20 - 0.025Q

Equating both MR and MC

20 - 0.025Q = 3

Q = 680

To find the price we will use this quantity in the demand function

P = 20 - 0.0125Q

P = 20 - 0.0125(680)

P = 11.5

Nighttime

Demand function

P = 40 - 0.025Q

Profit is maximized where marginal revenue is equal to marginal cost, we have the marginal cost so we have to find out marginal revenue

To find marginal revenue we will use demand function by doubling the coefficient of Q

MR = 40 - 0.05Q

Equating both MR and MC

40 - 0.05Q = 3

Q = 740

To find the price we will use this quantity in the demand function

P = 40 - 0.025Q

P = 40 - 0.025(740)

P = 21.5

Profit

Daytime

Profit = Total Revenue - Total Cost

Total Revenue = Price x Quantity

Total Revenue = 11.5 x 680

Total Revenue = 7820

Total Cost = ATC x Quantity

Total Cost = 3 x 680

Total Cost = 2040

Profit = Total Revenue - Total Cost

Profit = 7820 - 2040

Profit = 5780

Nighttime

Profit = Total Revenue - Total Cost

Total Revenue = Price x Quantity

Total Revenue = 21.5 x 740

Total Revenue = 15910

Total Cost = ATC x Quantity

Total Cost = 3 x 740

Total Cost = 2220

Profit = Total Revenue - Total Cost

Profit = 15910 - 2220

Profit = 13690