7. two farmers, a and b, each apply 100 tons of manure on their fields. to reduce manure runoff, the government has decided to require a permit for each ton of manure applied. the government gives each farmer 50 permits. farmer a incurs losses of $25 for each ton of manure he does not apply, and farmer b incurs losses of $50 for each ton of manure he does not apply. what is the total cost of reducing runoff if firms are not allowed to buy and sell permits from each other? what is the total cost of reducing runoff if the firms are allowed to buy and sell permits from each other?

The monthly demand equation for an electric utility company is estimated to be p equals 60 minus left parenthesis 10 superscript negative 5 baseline right parenthesis x, where p is measured in dollars and x is measured in thousands of killowatt-hours. the utility has fixed costs of $3 comma 000 comma 000 per month and variable costs of $32 per 1000 kilowatt-hours of electricity generated, so the cost function is upper c left parenthesis x right parenthesis equals 3 times 10 superscript 6 baseline plus 32 x. (a) find the value of x and the corresponding price for 1000 kilowatt-hours that maximize the utility's profit. (b) suppose that the rising fuel costs increase the utility's variable costs from $32 to $38, so its new cost function is upper c 1 left parenthesis x right parenthesis equals 3 times 10 superscript 6 baseline plus 38 x. should the utility pass all this increase of $6 per thousand kilowatt-hours on to the consumers?