Consider a price-taking firm in the competitive industry for raw chocolate. The market demand and supply functions for raw chocolate are estimated to be
Chocolate demand: Q = 10,000-10,000P+2M
Chocolate supply: Q = 40,000 + 10,000P- 4,000PI
Where Q is the number of 10 pound bars per month, P is the price of a 10 pound bar of raw chocolate, income is M, and PI is the price of cocoa (the primary ingredient input).
The manager of ABC Cocoa Products uses time-series data to obtain the following forecasted values of M and PI for 2011:
M = $30,000 and PI = $15
The manager of ABC Cocoa also estimates its average variable cost function to be
AVC = 3.0-0.0028Q + 0.0000008Q2
Fixed costs at ABC will be $1,850 in 2011.
a) The price of raw chocolate in 2011 is forecasted to be
b) Average variable cost reaches its minimum value at ? bars of chocolate per month.
c) The minimum value of average variable cost is $
A) The price of raw chocolate in 2011 is forecasted to be
Chocolate demand: Q = 10,000 - 10,000P + 2M
Supply: Q = 40,000 + 10,000P- 4,000PI
Put PI = $15
Solution describes the steps to calculate price and minimum value of average cost in the given scenario.