Question

a) Always Round Tire hires Plain Truth Advertising to write copy for its newspaper advertisements. Always Round has a demand for advertising of MB = 400 − 2S where S is the number of hours that Plain Truth works. If Plain Truth has a fixed supply cost given by MC = $150 per hour, what are the number of hours that Always Round purchases from Plain Truth under the assumption of costless monitoring? How much is the contract worth to Always Round? If Always Round offers half of the surplus to Plain Truth as an incentive, how much is Plain Truth paid for the job?

b) Always Round Tire hires Plain Truth Advertising to write copy for its newspaper advertisements. Always Round has a demand for advertising of MB = 400 − 2S where S is the number of hours that Plain Truth works. If Plain Truth has a fixed supply cost given by MC = $150 per hour, what are the number of hours that Always Round purchases from Plain Truth? Now, if the copy writers are slackers and only deliver 100 hours of work each week, and if each company must spend $1,250 in monitoring and bonding costs, what is the surplus and residual loss in this environment?

Answer 1

For finding the optimum number of hours that should be purchased, do MB = MC

=> 400 - 2S = 150

=> S = 250 / 2

=> S = 125

For finding contract worth ( = Net Benefit ) see graph below

Net benefit to Always Round = Consumer surplus + producer surplus

Net benefit = Area of Pink

Net benefit = ( 1 / 2 ) * 125 * ( 400 - 150 )

Net benefit = 15625

If half of the surplus is transferred to Plain Truth, then let's see what will happen

area of Pink region = 1 / 2 * 15625 ( this is the surplus transferred to Plain Truth)

area of Blue = 1 / 2 * 15625

if the height of Blue is X, then its length would be 2X ( as the slope of line MB = 400 - 2S is -2. )

Finding X

Since Area ( Blue ) = 1 / 2 * 15625

=> 1 / 2 * X * 2X = 1 / 2 * 15625

=> X2 = 15625 / 2

=> X = 88.4

therefore, Price paid = 400 - 2X = 400 - 2 * 88.4 = 223.2

b. If workers give up to 100 hours of work then

( Note: company spending 1250 per week on monitoring and bonding, will not affect the marginal cost, this 1250 will act as an additional fixed cost per week, and we know that fixed cost doesn't affect marginal cost. )

if S can be maximum 100 which is less than optimal point S = 125 then, equilibrium will occur at S = 100 only as shown in the above graph.

at S = 100, Environmental loss ( or Deadweight loss ) is the pink region shown in graph ( = net benefit at the optimal point - net benefit at the constrained point.)

Environmental loss = 1 / 2 * ( 200 - 150 ) * ( 125 - 100 )

Environmental loss = 625

Surplus = 1 / 2 * 125 * ( 400 - 150 ) - 625

Surplus = 15000