Suppose that the market demand function for cows is

Upper Q equals $1$ comma $000$ comma $000$ p Superscript negative $2$Q$=1,000,000$p$2,$

where Q is the number of cows per month and p is the price per cow. The market supply function is

Upper Q equals pQ$=$p$.$

a$.$What are the equilibrium price and quantity of$$ cows? What is the consumer$$ surplus, the producer$$ surplus, and$$ welfare?

b$.$ Now, suppose that the government provides a subsidy of

$$$$100100$

per cow. What are the new equilibrium price and$$ quantity, the consumer$$ surplus, the producer$$ surplus, and$$ welfare?

Enter your responses below as whole numbers.

Part $2$

a$.$ The equilibrium price is

$$$enter your response here.