Question

A demand function for certain products is q = 300p + 10,000. The fixed expenses are $500,000, and the variable expenses are $2 per item product.

a) Express the expense function in terms of q.
b) If the price is set at $20, what quantity will be demanded?
c) If q = 1000 widgets, find E, the cost (expense) of producing them.
d) Use substitution to express the expense function in terms of p.
e) If the price is set at p = $15, how much will it cost to produce the correct number of widgets?

Answer 1

a) The expense function is E = (q * $2) + $500,000. b) If the price is set at $20, the quantity demanded is 6,000. c) If q = 1000 widgets, the cost of producing them is $502,000.

Step-by-step explanation:

a) The expense function can be expressed in terms of q by subtracting the fixed expenses from the quantity of items produced multiplied by the variable expenses per item. So the expense function is E = (q * $2) + $500,000.

b) If the price is set at $20, we can substitute this value into the demand function to find the quantity demanded: q = (300 * $20) + $10,000 = 6,000.

c) If q = 1000 widgets, we can substitute this value into the expense function to find the cost of producing them: E = (1000 * $2) + $500,000 = $502,000.

d) To express the expense function in terms of p, we can rearrange the demand function to solve for p: p = (q - 10,000) / 300.

e) If the price is set at p = $15, we can substitute this value into the expense function to find the cost of producing the correct number of widgets: E = (q * $2) + $500,000 = (q * $2) + $500,000.