A consulting firm specializing in agriculture determines that the following combinations of hay and grain consumption per lamb will result in a 25- pound gain for a lamb:

a. The firm's president wants to estimate the marginal product of a pound of grain in producing lamb. Can he do so on the basis of these data?
b. The firm's president is convinced that constant returns to scale prevail in lamb production. If this is true and hay and grain consumption per lamb are the only inputs, how much gain accrues if the hay consumption per lamb is 100 pounds and the grain consumption per lamb is 250.2 pounds?
c. What is the marginal rate of technical substitution of hay for grain when between 40 and 50 pounds of hay (and between 130.9 and 125.1 pounds of grain) are consumed per lamb? d. A major advance in technology occurs that allows farmers to produce a 25- pound gain per lamb with less hay and grain than the preceding table indicates. If the marginal rate of technical substitution (at each rate of consumption of each input) is the same after the technological advance as before, can you draw the new is quant corresponding to a 25- pound gain per lamb?

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Pounds of hay Pounds of grain 40 50 60 70 80 90 110 130 150 130.9 125.1 120.1 115.7 108.3 102.3 97.4 93.8