a. Draw a diagram to derive the Marginal Rate of Technical Substitution in production; and show that the ratio is equal to the ratio of marginal products of the inputs and the ratio of the inputs' prices. (4 marks) b. An economy consists of three workers. Laura, Lynnette and Lemuel. Each works 10, hours a day and can produce two services, baking breads and washing cars. In an hour, Laura can either bake 1 bread or wash 1 car. Lynnette can either bake 1 bread or wash 2 cars and Lemuel can either bake 2 breads or wash 1 car i. Calculate how much of each service is produced under the following circumstances, labelled A, B, C and D (4 marks) All three spend all their time baking breads (A) All three spend all their time washing cars (B) All three spend half their time on each activity (C) Laura spends half time on each activity, while Lynnette only washes cars and Lemuel only bakes breads (D) ii. Graph the production possibilities frontier for this economy. Use your answers in i) above to identify points A, B, C and D on your graph? (1 mark) iii. Explain why the production possibilities frontier for this economy has the shape it does (0.5 mark) iv. Are there any of the allocations calculated in i) above inefficient? (1 mark)
