Question

Bob Thomason produces theorems using hours of labor and Big Machines. In the short run, his labor is a variable factor but the number of Big Machines is fixed. When he works for L hours using M Big Machines, Bob can produce L·M theorems. There are only 3 Big Machines in the world, and they can only be rented in whole number quantities (you can not employ 1/2 of a Big Machine). Bob's time is worth $1 per hour, and it costs $1 per hour to rent a Big Machine. Draw Bob's short run total cost curve on the assumption that he employs 1 Big Machine. Do the same on the assumption that he employs 2 Big Machines. Do the same on the assumption that he employs 3 Big Machines. Draw Bob's long run total cost curve. Repeat questions 6 and 7 with “total cost" replaced by “average cost." Repeat questions 6 and 7 with “total cost" replaced by “marginal cost." Suppose that a firm experiences constant returns to scale at all levels of output. True or False: Whenever the firm increases its use of inputs, its output expands proportionately. Thus this firm never experiences diminishing marginal returns to labor. True or False: If the price of haircuts rises from $10 to $11, consumers' surplus will fall by 10%.

Answer 1

For plotting Bob's short run total cost curve with 1 Big machine,he will Produce Q output with L labor and cost is C=L*1$+L*M*$=L+ML=2L (i.e. total number of hours*1$ per hour for cost of labor+ total number of hours*M*1$ per hour for cost of M machines for L hours)

Now Q=LM=L

So cost curve with C on Y axis and Q on x axis is C=2L or y=2x

When he employs 2 Big machines,M=2

Q=LM=2L

C=L+ML=3L

so C=3Q/2 i.e. y=1.5x

Similarly when he employs 3 big machines,M=3

Q=LM=3L

C=L+ML=4L

C=4/3Q or y=1.333x

In the long run,he will employ all 3 big machines since the cost is minimum for that

i.e. long run cost curve c(q)=4/3Q

For finding average cost we divide the total cost by Q i.e. AC=2Q/2 for One big machine,1.5 for 2 big machines and 1.33 for 3 big machines

Similarly for finding marginal cost we differentiate the total cost by Q i.e. MC=d(2Q)/dQ=2 for one big machine,1.5 for 2 big machines and 1.33 for 3 big machines.

These are horizontal lines y=2,y=1.5 and y=1.33

False,when the firm increases its use of inputs, its outputs expands proportionately,that is true,but the firm still may experience diminishing returns of labor. Diminishing returns does not mean that all the inputs are increased proportionately. Multiplying both Capital and Labor by a factor of N will increase outputs by a factor of N which is constant returns of scale. However keeping capital constant and increasing Labor alone(or vice versa) will cause diminishing returns with decreasing marginal output of each additional labor (eg. keeping capital constant and increasing labor by let's say 30% will only increase the output by 10-15%,further increasing labor alone by 30% will increase the output even less)

False,the percentage change in the consumer surplus also depends on the demand function and its slope. There are many demand functions possible where the decrease in consumer surplus after the price goes from 10 to 11$ is not 10%