Jo has preferences described by the utility function, U = c0.5r0.5. Where c denotes her consumption...

Jo has preferences described by the utility function, U = c0.5r0.5. Where c denotes her consumption of carrots in ounces and r denotes her consumption of red meat in ounces. She faces two constraints,

1) she has an income of 1000 and the price of c is 10, while the price of r is 20.

2) due to health concerns, the government does not allow anybody to consume more than 80 ounces of r.

a) write down the Lagrangian and derive the first order and complementary slackness conditions. Use  as the Lagrange multiplier for constraint 1 and  as the Lagrange multiplier for constraint 2. (For simplicity, you can ignore non-negativity constraints for c and r).

b) you believe that at the optimum, the first constraint is binding and second constraint is slack. You find that c = 50 and r = 25. What else needs to be checked to verify that this is indeed the solution? Carry this(these) step(s) out.

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Expert Solution

Rahul Sunny answered 1 year ago

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