Production. Costs Problem 6 on p.194.

Production. Costs Problem 6 on p.194.

Production. Costs Problem 6 on p.194. MC = cost of making an extra unit

Production. Costs Problem 6 on p.194.

If cost is given as a function of Q, then For example: TC = 10,000 + 200 Q + 150 Q2 MC = ?

Profit is believed to be the ultimate goal of any firm. If the production unit described in the problem above can sell as many units as it wants for P=$360, what is the best quantity to produce (and sell)?

Doing it the “aggregate” way,by actually calculating the profit:

Doing it the “aggregate” way,by actually calculating the profit: P=$360

Alternative: The Marginal ApproachThe firm should produce only units that are worth producing, that is, those for which the selling price exceeds the cost of making them. < 360 > 360

Principle (Marginal approach to profit maximization): • If data is provided in discrete (tabular) form, then profit is maximized by producing all the units for which and stopping right before the unit for which

Principle (Marginal approach to profit maximization): • If data is provided in discrete (tabular) form, then profit is maximized by producing all the units for which MR > MCand stopping right before the unit for which MR < MC • In our case, price of output stays constant throughout therefore MR = P • (an extra unit increases TR by the amount it sells for) • If costs are continuous functions of QOUTPUT, then profit is maximized where

Principle (Marginal approach to profit maximization): • If data is provided in discrete (tabular) form, then profit is maximized by producing all the units for which MR > MCand stopping right before the unit for which MR < MC • In our case, price of output stays constant throughout therefore MR = P • (an extra unit increases TR by the amount it sells for) • If costs are continuous functions of QOUTPUT, then profit is maximized where MR=MC

What if FC is $100,000 instead of $10,000? How does the profit maximization point change?

Principle: Fixed cost does not affect the firm’s optimal short-term output decision and can be ignored while deciding how much to produce today. Consistently low profits may induce the firm to close down eventually (in the long run) but not any sooner than your fixed inputs become variable ( your building lease expires, your equipment wears out and new equipment needs to be purchased, you are facing the decision of whether or not to take out a new loan, etc.)

Sometimes, it is more convenient to formulate a problem not through costs as a function of output but through output (product) as a function of inputs used. Problem 2 on p.194. “Diminishing returns” – what are they? In the short run, every company has some inputs fixed and some variable. As the variable input is added, every extra unit of that input increases the total output by a certain amount; this additional amount is called “marginal product”. The term, diminishing returns, refers to the situation when the marginal product of the variable input starts to decrease (even though the total output may still keep going up!)

Total output, or Total Product, TP Amount of input used Range of diminishing returns Marginal product, MP Amount of input used

Calculating the marginal product (of capital) for the data in Problem 2:

In other words, we know we are in the range of diminishing returns when the marginal product of the variable input starts falling, or, the rate of increase in total output slows down. (Ex: An extra worker is not as useful as the one before him) Implications for the marginal cost relationship: Worker #10 costs $8/hr, makes 10 units. MCunit =

In other words, we know we are in the range of diminishing returns when the marginal product of the variable input starts falling, or, the rate of increase in total output slows down. (Ex: An extra worker is not as useful as the one before him) Implications for the marginal cost relationship: • Worker #10 costs $8/hr, makes 10 units. MCunit = $0.80 Worker #11 costs $8/hr, makes …

In other words, we know we are in the range of diminishing returns when the marginal product of the variable input starts falling, or, the rate of increase in total output slows down. (Ex: An extra worker is not as useful as the one before him) Implications for the marginal cost relationship: • Worker #10 costs $8/hr, makes 10 units. MCunit = $0.80 Worker #11 costs $8/hr, makes 8 units. MCunit =

In other words, we know we are in the range of diminishing returns when the marginal product of the variable input starts falling, or, the rate of increase in total output slows down. (Ex: An extra worker is not as useful as the one before him) Implications for the marginal cost relationship: • Worker #10 costs $8/hr, makes 10 units. MCunit = $0.80 Worker #11 costs $8/hr, makes 8 units. MCunit = $1 In the range of diminishing returns, MP of input is falling and MC of output is increasing

Marginal cost, MC Amount of output This amount of output corresponds to thisamount of input Marginal product, MP Amount of input used

When MP of input is decreasing, MC of output is increasing and vice versa. Therefore the range of diminishing returns can be identified by looking at either of the two graphs. (Diminishing marginal returns set in at the max of the MP graph, or at the min of the MC graph)

Back to problem 2, p.194. To find the profit maximizing amount of input (part d), we will once again use the marginal approach, which compares the marginal benefit from a change to the marginal cost of than change. More specifically, we compare VMPK, the value of marginal product of capital, to the price of capital, or the “rental rate”, r.

Back to problem 2, p.194. To find the profit maximizing amount of input (part d), we will once again use the marginal approach, which compares the marginal benefit from a change to the marginal cost of than change. More specifically, we compare VMPK, the value of marginal product of capital, to the price of capital, or the “rental rate”, r. > > > > > STOP <

Why would we ever want to be in the range of diminishing returns? Consider the simplest case when the price of output doesn’t depend on how much we produce. Until we get to the DMR range, every next worker is more valuable than the previous one, therefore we should keep hiring them. Only afterwe get to the DMR range and the MP starts falling, we should consider stopping.Therefore, the profit maximizing point is always in the diminishing marginal returns range! Surprised?

Production. Costs Problem 6 on p.194.