Is there a production function with two outputs using a single input ("money") with increasing returns to scale but diseconomies of scope?

• The production function associated with the cost functionC(x,y)=x+y
• The production function associated with the cost functionC(x,y)=xy
• The production function associated with the cost functionC(x,y)=x+y
• The production function associated with the cost functionC(x,y)=x+y+xy
• Such a production function exists, but none are listed above
• No such production function exists

Our firm has economies of scope in tires and water bottles. The market for water bottles is competitive, and in the short run we are producing atP=MC. The demand for tires has increased and as a result we are producing more tires.

What happens to our production of water bottles?

• Production of water bottles increases
• Production of water bottles remains the same
• Production of water bottles decreases
• The effect on production of water bottles cannot be determined from provided information