Economics Assignment-Microeconomics

1.

a)

At the current price, $1.50, the theatre would sell 225 tickets.

If  then[pic 1]

[pic 2]

[pic 3]

[pic 4]

b)

[pic 5]

The marginal revenue curve is a derivative of the total revenue curve. To calculate total revenue, the demand curve needs to be solved for price rather than quantity (inverse demand curve)

If ,   then[pic 6]

[pic 7]

[pic 8]

[pic 9]

[pic 10]

The derivative of TR with respect to quantity will be the marginal revenue equation.

[pic 11]

c)

For a profit-maximizing outcome,     (see graph 1)[pic 12]

The costs of the theater are fixed. To identify the fixed cost, determine what the cost is for producing zero output. Fixed cost is incurred whether or not any output is produced (in this case, whether any tickets are being sold or not).

When [pic 13]

[pic 14]

[pic 15]

[pic 16]

Therefore, fixed costs would be $3.

With no variable costs, the total costs would be equal to the fixed cost and the marginal cost would be zero. (The change in total cost for each additional ticket sold would be zero).

Alternatively, the total costs, TC = 3.

The derivative of the total cost curve equals the marginal cost.

In this case, the derivative of TC=0.

If marginal costs =0 and profit maximization occurs when , then [pic 17]

[pic 18]

[pic 19]

[pic 20]

Therefore, profit maximization occurs when 225 tickets are sold.

At this point, there is the largest difference between revenue and costs.

d)

The price elasticity of demand at this point will be equal to 1.

This point (225 tickets sold for $1.50) represents the halfway point along the demand curve (where total revenue is at its maximum, see graph 2) and the elasticity of demand will be 1.

[pic 21]

[pic 22]

[pic 23]

[pic 24]

Using equation 3,

The point elasticity of demand when tickets are priced at $1.50 and 225 tickets are sold:

[pic 25]

[pic 26]

[pic 27]

[pic 28]

[pic 29]

Rule of optimality?????????????????