Question

In: Economics

assume the shadow cost is $52 per hour. For B7, assume allocated fixed costs of $1391...

assume the shadow cost is $52 per hour. For B7, assume allocated fixed costs of $1391 and variable costs of $13 per unit. B7 uses 0.13 hours of inspector time per unit and has a demand curve of V = 1000 - 28P. What is the optimal price to charge for B7? The answer must be rounded to cents

Solutions

Expert Solution

The optimal price is at the equality of MR and MC, called equilibrium.

Given,

V = 1000 – 28P

By rearranging,

28P = 1000 – V

P = 1000/28 – V/28 …………. Price function

TR = P × V = (1000/28 – V/28) × V

= 1000V/28 – V^2/28

Now, MR is the derivative with respect to V of above.

MR = (d/dV) (1000V/28 – V^2/28)

= 1000/28 – (2/28)V

Given, MC = Variable cost per unit + Fixed cost per unit

= 13 + (1391 × 0.13)

= 13 + 180.83

= 193.83

Hence,

MR = MC

1000/28 – (2/28)V = 193.83

1000/28 – 193.83 = (2/28)V

35.714 – 193.83 = (2/28)V

-158.11571 × (28/2) = V

V = - 2,213.61994

This is to be placed in the price function

P = 1000/28 – V/28 …………. Price function

= 1000/28 – (-2213.61994/28)

= 1000/28 + 2213.61994/28

= 3213.61994/28

= 114.77 (rounded to nearest cent)

Answer: optimal price is $114.77.

Note: the shadow price or anticipated price is very low.

Rahul Sunny answered 2 years ago

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