Answer to Question #181375 in Microeconomics for Romy

Question

Could you assist with the following?

Suppose that the price of whiskey increases from R100 to R150 a bottle and as a result the Qd decreases from 1 100 bottles to 800 bottles.  

5.1. Use the ARC (midpoint) formula to calculate the price elasticity of demand for whiskey. 

5.2. Use the income elasticity of demand to distinguish between a normal good and an inferior good. In your explanation, provide the correct elasticity coefficient for each product and the relationship between income and quantity demanded. 

8.Perfect competition occurs when none of the individual market participants (buyers and sellers) can influence the price of the product. Under perfect competition, marginal revenue and average revenue are thus both equal to the market price. The situation in which a firm makes an economic profit is identified as one of the possible short-run positions of a firm under perfect competition. Illustrate the given short-run position and explain the situation with reference to your graph. 

Answer 1

Solution:

5.1: Mid-point formula to calculate the price elasticity of demand for whiskey

Elasticity of demand = $\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; price}$

% change in qty demanded = $\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \times 100 = \frac{800 -1100}{(800+1100)/2 } \times 100$

$\frac{-300}{950} \times 100 = -0.316\times 100 = -31.6\%$

% change in price =$\frac{P_{2} -P_{1}}{(P_{2}+P_{1})/2 } \times 100 = \frac{150 -100}{(150+100)/2 } \times 100$

$\frac{50}{125} \times 100 = 0.4\times 100 = 40\%$

Elasticity of demand = $\frac{-31.6\%}{40\%} = 0.79$

The elasticity of demand is less than 1, which means that whiskey is price inelastic.

 

5.2: Distinguish between a normal good and an inferior good using the income elasticity of demand.

A normal good is one whose demand rises as consumer income increases. On the other hand, an inferior good is a good whose demand decreases when consumer income rises, or increases when consumer income decreases.

The elasticity coefficient for a normal good: YED>0 (Income elasticity of demand is positive but less than one).

The elasticity coefficient for an inferior good: YED<0 (Income elasticity of demand is negative and less than one)

 

8. A firm is able to make economic profit in the short run when it sets its price equal to average revenue and marginal revenue and when that particular price is greater than the average total cost. The firm is making an economic (supernormal) profit as displayed on the graph since the marginal revenue exceeds marginal cost, which allows it to increase its output.

The firm’s price is equal to its average revenue and marginal revenue and it is above the average cost as depicted by the below graph.