Question

George has been selling 5,000 T-shirts per month for $8.50. When he increased the price to $9.50, he sold only 4,000 T-shirts. What is the demand elasticity? If his marginal cost is $4 per shirt, what is his desired markup and what is his initial actual markup? Was raising the price profitable?

Answer 1

Calculation for demand elasticity;

$\Epsilon_d =\frac{Q_1-Q_2} {Q_1+Q_2} * \frac{P_1+P_2} {P_1-P_2}$

$\Epsilon_d =\frac{5000-4000} {5000+4000} * \frac{8.5+9.5} {8.5-9.5}$

$E_d=\frac {1} {9}*(-18)$

$E_d= \boxed{-2}$

Demand elasticity is -2

Initial actual markup percentage calculation;

$IMP= \frac {Sales Price-Marginal Cost} {Marginal Cost} *100$

$IMP= \frac {8.50-4.00} {4.00} *100$

$IMP= \boxed{112.5\%}$ %

Desired markup percentage calculation;

$DMP= \frac {Sales Price-Marginal Cost} {Marginal Cost} *100$

$DMP= \frac {9.50-4.00} {4.00} *100$

$DMP= \boxed{137.5\%}$ %

Profit of selling 5000 T shirts on markup price;

$Profit= N * (Sales Price-Marginal Cost)$

$Profit=5000 * (8.50-4.00)$

$Profit= \boxed{22500.00}$

Profit of selling 4000 T shirts on markup price;

$Profit= N * (Sales Price-Marginal Cost)$

$Profit= 4000 * (9.50-4.00)$

$Profit= \boxed{22000.00}$

Raising the price of T shirt is not profitable. $(22000<22500)$