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# Calculating minimum value of AVC

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 \$

#### Solution Preview

A) The price of raw chocolate in 2011 is forecasted to be
Chocolate demand: Q = 10,000 - 10,000P + 2M
Put M=\$30000
Demand Q=10000-10000P+2*30000
=10000-10000P+60000
=70000-10000P
Supply: Q = 40,000 + 10,000P- 4,000PI
Put PI = \$15
Supply Q=40000+10000P-4000*15
=40000+10000P-60000
=-20000+10000P
In ...

#### Solution Summary

Solution describes the steps to calculate price and minimum value of average cost in the given scenario.

\$2.19