Question

COST & PRODUCTION FUNCTIONS

In order to reduce unit cost, the CEO of ABC Corporation has to decide whether to increase or decrease total production. A marketing analyst has reported the following information about ABC Corporation’s cost and production structure:

Year	Total Cost (TC) ($1000)	Quantity Produced (Q) (Unit)
2018	2	10
2019	4	15
2020	6	35

1.Use Ordinary Least Squares Method (OLS) to estimate the ABC Corporation’s total cost function; that is, TC =β +βQ;

2. What is ABC Co’s marginal cost?

3. What is ABC Co’s fixed cost?

4. Calculate the scale elasticity at the mean of the data

5. In order to reduce the unit cost would you recommend an increase or a decrease in total production? Why?

Answer 1

1)

The OLS regression to estimate total cost function TC = b1 +b2Q is:

Year	Total Cost (TC) ($1000)	Quantity Produced (Q) (Unit)		SUMMARY OUTPUT
2018	2	10
2019	4	15		Regression Statistics
2020	6	35		Multiple R	0.944911183
				R Square	0.892857143
				Adjusted R Square	0.785714286
				Standard Error	0.9258201
				Observations	3
				ANOVA
					df	SS	MS	F	Significance F
				Regression	1	7.142857143	7.142857143	8.333333333	0.212295615
				Residual	1	0.857142857	0.857142857
				Total	2	8
					Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
				Intercept	1.142857143	1.124858268	1.016001016	0.49494725	-13.14982231	15.43553659	-13.14982231	15.43553659
				Quantity Produced (Q) (Unit)	0.142857143	0.049487166	2.886751346	0.212295615	-0.485936919	0.771651205	-0.485936919	0.771651205

Hence, the TC = 1.14285714285714 + 0.142857142857143*Q

2.

The marginal cost is: dTC/dQ = 0.142857142857143

3.

The fixed cost is the cost when Q=0, that is, Total Fixed Cost = 1.14285714285714

4.

The scale elasticity at mean Q =20 and TC = 4 is:

(dTC/dQ)*(Q/TC)

= 0.142857142857143*(20/4) = 0.714285714

5.

The per unit Cost = TC/Q = (1.14285714285714/Q) + 0.142857142857143

Thus, in order to reduce the unit cost, the firm should increase the production, as with Q increasing, TC/Q = per-unit cost decreases