Answer to Question #312809 in Macroeconomics for Huhii

Question

For the given demand equation Qd=30-2p. Calculate the inverse of the demand equation, Average Revenue, Total Revenue and Marginal Revenue

b) You are trying to decide whether to take a vacation. Most of the costs of the vacation (airfare, hotel, and forgone wages) are measured in dollars, but the benefits of the vacation are psychological. How can you compare the benefits to the costs?

Answer 1

a)Linear demand equation:

Q = a-bP

Qd = 30-2P

Therefore, Inverse demand equation will be:

Q = a-bP

bP = a-Q

P =$\frac{a}{b}- \frac{Q}{b}$

P =$\frac{a-Q}{b}$

Where;

a=intercept where P is 0,

b=slope of demand curve

P= Price

Given: a = 30

b = 2

Substitute in the equation

$P =\frac {a-Q}{b}$

P = (30 – Q) ÷ 2

P = 30/2 – 1/2

P = 15 –0.5Q

Therefore, inverse demand equation is P = 15-0.5Q

b)

i)Average Revenue (AR) = Price (P)

Therefore, average revenue is 15 - 0.5Q

Total Revenue (TR) = Price(P)$\times$Quantity demanded(Q)

= (15 - 0.5Q)$\times$ Q

= 15Q - 0.5_Q 2 

ii)Marginal Revenue (MR) will be the first derivative of TR

Therefore, MR =$\frac{d(TR)}{d(Qd)}$

= d(15Q - 0.5Q² )$\frac{15Q - 0.5Q^2}{Qd}$

=15-Q

Therefore, the Marginal Revenue is 15-Q

c) The benefits of a vacation will vary from person to person. Most people associate a vacation with relaxation, peace and a chance to spend quality time with family. If a person feels they need these psychological benefits then the costs of a vacation may be worth it.

When you spend money for pleasure the cost question is not counted because here the cost has no value as this money is spent for your pleasure which is a psychological matter and hence comparing the cost to Benefits never arise here.

At the maximum you can say is that it is an opportunity cost for you and if the vacation gives you more psychological benefits then we can say the cost is cheaper compared to the benefits.