Question

B. The table below shows the total cost incurred by the firm operating in perfectly competitive market. Quantity (coats per day) Total cost (per coat) $1.410 8 1,640 9 1,910 10 2,210 11 2,560 The price of a coat is $285. How many coats per day should the firm produce to maximize economic profit? (Show detailed calculations below) 9. A fall in the price of X from €12 to €8 causes an increase in the quantity of Y demanded from 900 to 1,100 units a) What is the cross elasticity of demand between products X and Y? b) Are products X and Y most likely substitutes or complements and why?

Answer 1

Question 8

A perfectly competitive market is a type of market structure where there are many buyers and sellers of goods in the market. The producers are price takers because the price is decided by market forces and not individual firms and all the firms produce homogeneous goods.

The profit-maximizing output level in a perfectly competitive firm is at the point where Price = Marginal cost. Marginal cost is the additional cost incurred for producing one extra unit of output.

In the table, we are given total cost and quantity and we can find the marginal cost as follows:

The marginal cost for producing nth unit = (TCⁿ - TC^n-1) / [n-(n-1)]

Here, TCⁿ = Total cost of the nth unit and TC^n-1 is the total cost of (n-1) unit.

Marginal cost for producing 8th unit = (1640-1410)/(8-7)

= $230

Like this we can find marginal cost for producing different units:

Quantity (coats per day)	Total cost (per coat)	Marginal cost
7	1410	-
8	1640	230
9	1910	270
10	2210	300
11	2560	350

For the firm to make profits, its price should be at least greater than the marginal cost, we can see that MC cannot be 300 or 350 (since price = $285). Thus the closest marginal cost would be 270 (which is less than price = 285 and thus the firm can make an economic profit).

Corresponding to a marginal cost of $270, the firm is producing 9 units thus the firm will produce 9 units of coats per day to maximize economic profit.

Question 9

Cross price elasticity of demand tells us the responsiveness of change in quantity demanded of good X due to the change in prices of good Y. If the cross-price elasticity of demand is positive that means the two goods are substitutes and if the number is negative the goods are complements to each other.

We know substitute goods are the one that is alternative of each other like tea and coffee, if prices of tea increases, people will switch to coffee. This means an increase in the price of one good lead to increase in the quantity demanded of another good (positive cross price elasticity of demand).

Complements are the goods that are used together like car and petrol. If the prices of petrol increases, the quantity demanded of cars will decrease. This means that an increase in the price of one good lead to a decrease in the quantity demanded of another (negative cross-price elasticity of demand).

Cross price elasticity of demand is calculated by the following formula:

Cross price elasticity of demand = % change in quantity demanded of Y/ % change in the price of X

% change in the quantity demanded of Y = (1100-900)/900 *100

= 22.22%

% change in the price of good X = (8-12)/ 12 *100

= -33.33%

Thus, the cross-price elasticity of demand = 22.22% / -33.33% = -0.66

We can see that the cross-price elasticity of demand is negative which means that the goods X and Y are complements to each other. This means they are brought together in a way that the fall in the price of one good lead to rise in quantity demanded of another good.