Asked by Lauren Knight on Jun 17, 2024
Verified
Estimates of the industry long-run average cost of producing a type of plastic hook were made in 1970 and again in 1985. Estimates of these relationships are presented as:
LAC70 = 10 - 0.3Q + 0.05Q2
LAC85 = 8 - 0.6Q + 0.04Q2,
where Q is output in hundreds of cases per day, and LAC is average cost in dollars per unit. Assume that costs are expressed in inflation adjusted or constant dollars. From the information available, can you learn anything about economies of scope, economies of scale, and a learning curve in this industry? Explain. Do these curves reveal anything about the state of technology in this industry? Explain.
Economies of Scope
Economies of scope describe cost advantages that enterprises obtain due to a broader scope of operations, where producing a wider variety of goods or services leads to lower average costs.
Economies of Scale
Reductions in the average cost of a product in the long run, resulting from increased production and operational efficiencies.
Learning Curve
The concept that describes how new skills or knowledge can be acquired more efficiently over time, leading to decreased costs and increased productivity.
- Understand the concept of economies of scale and scope.
- Analyze long-run cost functions and their dependencies on output and experience.
- Evaluate the impact of technological changes and experience on production costs.
Verified Answer
VA
Velaine AristylJun 23, 2024
Final Answer :
Nothing can be learned about economies of scope, given that only one product is being produced. We can get some idea about technology by calculating the output rate that produces a minimum LAC. For the two points in time, the minimum LAC is calculated as follows:
For 1970:
LA
70 = -0.3 + 0.1Q = 0
Q = 3.0 (in hundreds of cases)
For 1985:
LA
85 = -0.6 + 0.08Q = 0
Q = 7.5 (in hundreds of cases)
The LAC70 at Q = 3 is 10 - 0.3(3) + 0.05(3)2 = $9.55/case.The LAC85 at Q = 7.5 is 8 - 0.6(7.5) + 0.04(7.5)2 = $5.75/case.We see that LAC is minimized at positive levels of Q in 1970 and in 1985. Also, we see that LAC is minimized at a higher level of output in 1985 than in 1970. Over time the rate of production in the industry that represented the optimum scale of plant increased. The fact that LAC decreased time for various levels of output (LAC70 vs. LAC85) indicates that technology changed (improved) and/or that there was a learning process in progress (learning curve). The data given do not allow one to separate the two effects. Since both LAC functions have minimums, economies of scale are evident. Economies occur to Q = 3 (1970) and Q = 7.5 (1985).
For 1970:
LA
70 = -0.3 + 0.1Q = 0Q = 3.0 (in hundreds of cases)
For 1985:
LA
85 = -0.6 + 0.08Q = 0Q = 7.5 (in hundreds of cases)
The LAC70 at Q = 3 is 10 - 0.3(3) + 0.05(3)2 = $9.55/case.The LAC85 at Q = 7.5 is 8 - 0.6(7.5) + 0.04(7.5)2 = $5.75/case.We see that LAC is minimized at positive levels of Q in 1970 and in 1985. Also, we see that LAC is minimized at a higher level of output in 1985 than in 1970. Over time the rate of production in the industry that represented the optimum scale of plant increased. The fact that LAC decreased time for various levels of output (LAC70 vs. LAC85) indicates that technology changed (improved) and/or that there was a learning process in progress (learning curve). The data given do not allow one to separate the two effects. Since both LAC functions have minimums, economies of scale are evident. Economies occur to Q = 3 (1970) and Q = 7.5 (1985).
Learning Objectives
- Understand the concept of economies of scale and scope.
- Analyze long-run cost functions and their dependencies on output and experience.
- Evaluate the impact of technological changes and experience on production costs.