Question

Cliff’s Cams (CC) makes cams (surprise!). The average production cost per cam is estimated at $40 + 15/2x (where x is the number of cams produced and sold). CC can currently sell 20 cams at $80 each. What is the current profit of the firm? What is the marginal cost of producing one more cam? If a new buyer offers to buy an additional 10 cams at $60 each, then what is the new firm profit? What if our current customers then demand the same discount, what is firm profit?

Answer 1

Currently CC is manufacturing and selling 20 Cams and selling it at $80 per Cams

Cost of producing 20 Cams

= Number of cams* ( $40 + 15/2*20) =20 [ $40 + $0.375 0] = 20 [ $ 40.375 ] =807.5

Each can is sold at $80 each.

Total sales value of 20 Cans : $80* 20 Cams = $1600

Total Profit on sale of 20 cams = Total Sales value - Total Cost

= $1600 - $807.5 = $ 792.5

Current Profit of Firm is $792.5

Marginal Cost of producing 1 more Cam

Total Cost for producing 21 cams

= 21 [ $40 + 15/2*21 ]

= 21 [ $40 + $0.3571 ]

= $847.5

Marginal cost of producing one more Cam

= Total Cost to produce 21 cams - Total cost of producing 20 Cams

= $847.5 - $807.5

= $40

Currently Firm is producing 20 Cams and a new customer for 10 Cams is being approached then

Cost of producing 10 additional cams is

= Total cost of producing 30 cams - Total cost of producing 20 cams

= [30* ( $40 + 15/2*30) ] -

= $1207.5 - $807.5

= $400

Profit on Sale of 10 Cams

= Sale Value - Cost value

= [10*$60] - $400

= $200

Selling price for 10 Cams is $60 and if our existing customers for 20 cams demand for same discount then amount of discount provided will be

= $20 for each cam

=$20 * 20 cam

=$ 400

Firms New profit

= [ Existing previous profit - Discount ] + Additional profit on sale of 10 Cams

= [ $ 792.5 - $ 400 ] + $ 200

= $ 592.5